On Exponential Sums Related to the Circle Problem

• Date: 2004
• Main Authors: Slezeviciene, R., Steading, J., Шлечевичен, Р., Штедін, Й.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2004
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3853
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Let r(n) count the number of representations of a positive integer n as a sum of two integer squares. We prove a truncated Voronoi-type formula for the twisted Mobius transform $$\mathop \sum \limits_{n \leqslant x} \;\,r(n)\;\exp \left( {2\pi i\frac{{nk}}{{4l}}} \right),$$ where k and l are pos...